document.write( "Question 422417: Hey\r
\n" ); document.write( "\n" ); document.write( "Given that sinx(cosy + 2siny) - cosx(2cosy-siny) = 0, find the value of tan(x+y)\r
\n" ); document.write( "\n" ); document.write( "Thanks! \n" ); document.write( "

Algebra.Com's Answer #294860 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!
Given that sinx(cosy + 2siny) - cosx(2cosy-siny) = 0, find the value of tan(x+y)\r
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "        sinx(cosy + 2siny) - cosx(2cosy - sin y) = 0\r\n" );
document.write( "\r\n" );
document.write( "Remove the parentheses:\r\n" );
document.write( "\r\n" );
document.write( " sinx*cosy + 2sinx*siny - 2cosx*cosy + cosx*siny = 0\r\n" );
document.write( "\r\n" );
document.write( "Rearrange the terms:\r\n" );
document.write( "\r\n" );
document.write( " sinx*cosy + cosx*siny - 2cosx*cosy + 2sinx*siny = 0\r\n" );
document.write( "\r\n" );
document.write( "Factor -2 out of the 3rd and 4th terms:\r\n" );
document.write( "\r\n" );
document.write( "sinx*cosy + cosx*siny - 2(cosx*cosy - sinx*siny) = 0\r\n" );
document.write( "\r\n" );
document.write( "Use the identity sin(A + B)=sinA*cosB + cosA*sinB to rewrite the\r\n" );
document.write( "first two terms:\r\n" );
document.write( "\r\n" );
document.write( "           sin(x + y) - 2(cosx*cosy - sinx*siny) = 0\r\n" );
document.write( "\r\n" );
document.write( "Use the identity cos(A + B)=cosA*cosB - sinA*sinB to rewrite the\r\n" );
document.write( "two terms inside the parenthese:\r\n" );
document.write( "\r\n" );
document.write( "                       sin(x + y) - 2*cos(x + y) = 0\r\n" );
document.write( "\r\n" );
document.write( "Divide through by cos(x + y)\r\n" );
document.write( "\r\n" );
document.write( "                       sin(x + y)   2*cos(x + y)       0 \r\n" );
document.write( "                       覧覧覧覧覧 - 覧覧覧覧覧覧 = 覧覧覧覧覧\r\n" );
document.write( "                       cos(x + y)    cos(x + y)    cos(x + y)\r\n" );
document.write( "\r\n" );
document.write( "                  sin(A)  \r\n" );
document.write( "Use the identity  覧覧覧 = tan(A)\r\n" );
document.write( "                  cos(A) \r\n" );
document.write( "\r\n" );
document.write( "to rewrite the first term, and simplify the other terms:\r\n" );
document.write( "\r\n" );
document.write( "                                  tan(x + y) - 2 = 0\r\n" );
document.write( "\r\n" );
document.write( "                                      tan(x + y) = 2 \r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "

\n" );